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Some remarks on Wiener index of oriented graphs

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  • Knor, Martin
  • Škrekovski, Riste
  • Tepeh, Aleksandra

Abstract

In this paper, we study the Wiener index (i.e., the total distance or the transmission number) of not necessarily strongly connected digraphs. In order to do so, if there is no directed path from u to v, we follow the convention d(u,v)=0, which was independently introduced in several studies of directed networks. Under this assumption we naturally generalize the Wiener theorem, as well as a relation between the Wiener index and betweenness centrality to directed graphs. We formulate and study conjectures about orientations of undirected graphs which achieve the extremal values of Wiener index.

Suggested Citation

  • Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Some remarks on Wiener index of oriented graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 631-636.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:631-636
    DOI: 10.1016/j.amc.2015.10.033
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    Citations

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    Cited by:

    1. Andova, Vesna & Orlić, Damir & Škrekovski, Riste, 2017. "Leapfrog fullerenes and Wiener index," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 281-288.
    2. Knor, Martin & Majstorović, Snježana & Škrekovski, Riste, 2018. "Graphs preserving Wiener index upon vertex removal," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 25-32.
    3. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.
    4. Spiro, Sam, 2022. "The Wiener index of signed graphs," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    5. Hriňáková, Katarína & Knor, Martin & Škrekovski, Riste, 2019. "An inequality between variable wiener index and variable szeged index," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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